1 Caption: Prague, 1605.1 Johannes Kepler: Aha! Tycho's observations lead to four laws of planetary motion! Firstly, the planets move in ellipses, not circles!2 Johannes Kepler: Secondly, they sweep out equal areas in equal times. Thirdly, the square of the period is as the cube of the major radius. And fourthly and most importantly...3 SFX: ZUUURCH!! {time machine appears}4 Isaac Newton: Johannes Kepler?4 Johannes Kepler: Yes? Err... sorry, what was I thinking just now?

Planets orbit the sun in elliptical paths, with the sun at one focus of the ellipse.

The area of the ellipse that a planet sweeps out in its orbit for any given time interval is a constant. (This means that a planet moves faster when closer to the sun, and slower when further away.)

The square of the orbital period is proportional to the cube of the long axis of the ellipse.

These laws were empirically based on observations, not worked out theoretically. Kepler used the observations of
Tycho Brahe, at the time the best and most comprehensive set of astronomical
observations available in the world. They were accurate enough to allow Kepler to finally divest science of the mystically based notion that the planets
must move in circles (the reasoning being that otherwise the heavens would not be "perfect").

A theoretical basis for Kepler's laws had to wait for a certain Isaac Newton. Nevertheless, Kepler's deductions played a crucial part in
the unravelling of the mysteries of planetary motion.

Kepler lived the last years of his life in Regensburg, Germany - a town I visited in 2007. Naturally I visited his home, which has since been
turned into a small museum. I took the photo at right in an upstairs room - probably Kepler's bedroom. Being a 17th century house, the building
is slightly cramped by modern standards, and the walls and floors have subsided and settled a bit. In particular, there is a beam over
the staircase that is a bit low, and I banged my head into it while walking down the stairs.

I like to think that Johannes Kepler himself also banged hs head into that very same beam on a few occasions.